Computational Study of the Free Flight of a Flapping Wing at Low Reynolds Numbers

The application of computational aerodynamics for the design of micro aerial vehicles is increasingly becoming popular. One such area that has achieved good progress is in the development of tools for simulating moving bodies in low Reynolds number flow conditions with specified body kinematics. Using numerical and experimental data, scientists have been able to understand the basic mechanism of force generation in flapping airfoils and wings. However there is a paucity of experimental or computational studies for the free flight of a flapping wing in the literature. This work addresses the problem of free flight of a flapping wing aimed at understanding the combined effects of various flapping modes on thrust and lift generation. Solutions to the unsteady incompressible Navier Stokes equations coupled with rigid body dynamics on moving overlapping meshes are obtained at low Reynolds number flight. Trajectories are computed for a flapping wing with different modes of oscillation. It is observed that, independent periodic oscillation of wings produces less thrust compared to the combined oscillation modes. The effect of initial conditions on forward motion is also analyzed. Vorticity plots and particle traces show interesting flow patterns in the vicinity of the wing.

[1]  Tapan K. Sengupta,et al.  An improved method for calculating flow past flapping and hovering airfoils , 2005 .

[2]  H. Lugt,et al.  Autorotation of an elliptic cylinder about an axis perpendicular to the flow , 1980, Journal of Fluid Mechanics.

[3]  Wei Shyy,et al.  Flapping and flexible wings for biological and micro air vehicles , 1999 .

[4]  Dominic D. J. Chandar,et al.  Numerical Study of Unsteady Low Reynolds Number Aerodynamics of Airfoils and Wings using Moving Overlapping Meshes , 2007 .

[5]  Elisha Moses,et al.  From Flutter to Tumble: Inertial Drag and Froude Similarity in Falling Paper , 1998 .

[6]  W. Henshaw,et al.  Composite overlapping meshes for the solution of partial differential equations , 1990 .

[7]  Max F. Platzer,et al.  Computational Study of Flapping Airfoil Aerodynamics , 2000 .

[8]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[9]  Mao Sun,et al.  Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. , 2002, The Journal of experimental biology.

[10]  Mao Sun,et al.  Aerodynamic properties of a wing performing unsteady rotational motions at low Reynolds number , 2001 .

[11]  Max F. Platzer,et al.  Thrust Generation due to Airfoil Flapping , 1996 .

[12]  Daniel J. Quinlan,et al.  OVERTURE: An Object-Oriented Software System for Solving Partial Differential Equations in Serial and Parallel Environments , 1997, PPSC.

[13]  C. M. Dohring,et al.  Experimental and Computational Investigation of the Knoller-Betz Effect , 1998 .

[14]  William D. Henshaw,et al.  Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow , 2006, J. Comput. Phys..

[15]  Norman E. Hawk,et al.  Steady and Unsteady Motions and Wakes of Freely Falling Disks , 1964 .

[16]  Rainald Löhner,et al.  Fluid dynamics of flapping aquatic flight in the bird wrasse: three-dimensional unsteady computations with fin deformation. , 2002, The Journal of experimental biology.

[17]  C. Ellington The novel aerodynamics of insect flight: applications to micro-air vehicles. , 1999, The Journal of experimental biology.

[18]  Z. J. Wang,et al.  Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation. , 2004, Physical review letters.

[19]  Z. J. Wang,et al.  Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments , 2004, Journal of Experimental Biology.

[20]  Jun Zhang,et al.  Symmetry breaking leads to forward flapping flight , 2004, Journal of Fluid Mechanics.

[21]  Jun Zhang,et al.  On unidirectional flight of a free flapping wing , 2006 .

[22]  K. Kawachi,et al.  A Numerical Study of Insect Flight , 1998 .